Subgroups — C₂×C₁₃×#3402 #15747738

Order 3328.

1938 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	2	yes	maximal, complemented
2	C₁₃×#3402	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#497	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#495	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#464	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#462	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#463	C₂	1	2	yes	maximal
8	C₂×C₁₃×#446	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#440	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
17	C₁₃×#556	—	2	8	no	—
18	C₁₃×#556	C₂²	1	16	yes	complemented
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₁₃×#126	—	2	2	no	—
21	C₂×C₁₃×#126	—	2	2	no	—
22	C₂×C₁₃×#124	C₂²	1	2	yes	—
23	C₂×C₁₃×#124	C₂²	1	2	yes	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
29	C₂×C₁₃×#117	—	2	2	no	—
30	C₁₃×#497	C₂²	1	16	yes	complemented
31	C₁₃×#495	C₂²	1	8	yes	—
32	C₁₃×#464	C₂²	1	16	yes	complemented
33	C₁₃×#463	C₂²	1	16	yes	—
34	C₁₃×#462	C₂²	1	16	yes	complemented
35	C₁₃×#446	C₂²	1	8	yes	complemented
36	C₁₃×#440	C₂²	1	16	yes	complemented
37	C₄×C₁₃×Q₁₆	C₂²	1	8	yes	complemented
38	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#103	C₂²	1	2	yes	—
42	C₂×C₁₃×#103	C₂²	1	2	yes	—
43	C₂×C₁₃×#102	C₂²	1	2	yes	—
44	C₂×C₁₃×#97	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₃	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	—	2	4	no	—
52	C₂×C₁₃×Q₁₆	—	4	2	no	—
53	C₂×C₁₃×Q₁₆	—	4	4	no	—
54	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
55	C₂×C₁₃×Q₁₆	C₂³	1	4	yes	—
56	C₂×C₁₃×Q₁₆	C₂³	1	8	yes	—
57	C₂×C₁₃×SD₁₆	—	2	8	no	—
58	C₂×C₁₃×SD₁₆	—	4	4	no	—
59	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
60	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
61	C₂×C₁₃×D₈	—	4	2	no	—
62	C₂×C₁₃×D₈	C₂³	1	4	yes	—
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×C₄⋊Q₈	—	2	4	no	—
67	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	—
68	C₁₃×#126	—	2	16	no	—
69	C₁₃×#126	—	2	16	no	—
70	C₁₃×#124	—	2	4	no	—
71	C₁₃×#124	—	2	4	no	—
72	C₁₃×#124	C₂³	1	8	yes	—
73	C₁₃×#124	C₂³	1	8	yes	—
74	C₁₃×C₂²⋊Q₈	—	2	16	no	—
75	C₄×Q₈×C₁₃	—	2	4	no	—
76	C₄×Q₈×C₁₃	—	2	4	no	—
77	C₄×Q₈×C₁₃	D₄	1	4	yes	—
78	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
79	C₄×Q₈×C₁₃	C₂³	1	8	yes	—
80	C₄×Q₈×C₁₃	C₂³	1	4	yes	—
81	C₄×D₄×C₁₃	—	2	4	no	—
82	C₄×D₄×C₁₃	C₂³	1	8	yes	—
83	C₁₃×#117	—	2	16	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
92	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
93	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
94	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
96	C₂×C₄²×C₁₃	—	2	2	no	—
97	C₂×C₄²×C₁₃	—	2	2	no	—
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
100	C₁₃×#107	C₂³	1	4	yes	—
101	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
102	C₁₃×C₄⋊C₈	C₂³	1	4	yes	—
103	C₁₃×#103	C₂³	1	8	yes	—
104	C₁₃×#103	C₂³	1	8	yes	—
105	C₁₃×#102	C₂³	1	8	yes	—
106	C₁₃×#97	C₂³	1	8	yes	—
107	C₄×C₈×C₁₃	C₂³	1	4	yes	—
108	C₂×#3402	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂⁴×C₁₃	—	2	2	no	—
110	C₂×Q₈×C₁₃	—	2	2	no	—
111	C₂×Q₈×C₁₃	—	2	2	no	—
112	C₂×Q₈×C₁₃	—	2	4	no	—
113	C₂×Q₈×C₁₃	—	2	4	no	—
114	C₂×Q₈×C₁₃	—	2	4	no	—
115	C₂×Q₈×C₁₃	—	2	4	no	—
116	C₂×Q₈×C₁₃	—	4	2	no	—
117	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
118	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
119	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	—	2	4	no	—
122	C₂×D₄×C₁₃	—	2	4	no	—
123	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	8	no	—
128	C₂²×C₄×C₁₃	—	4	8	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×Q₁₆	—	2	8	no	—
135	C₁₃×Q₁₆	—	4	4	no	—
136	C₁₃×Q₁₆	—	4	8	no	—
137	C₁₃×SD₁₆	—	2	16	no	—
138	C₁₃×SD₁₆	—	4	8	no	—
139	C₁₃×D₈	—	4	4	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	4	no	—
142	C₂×C₈×C₁₃	#41	1	4	yes	—
143	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
144	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
145	C₂×C₈×C₁₃	C₂⁴	1	2	yes	—
146	C₁₃×C₄⋊C₄	—	2	8	no	—
147	C₁₃×C₄⋊C₄	—	2	8	no	—
148	C₁₃×C₄⋊C₄	—	2	8	no	—
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	C₂×D₄	1	8	yes	—
152	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
153	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
154	C₁₃×C₂²⋊C₄	—	2	8	no	—
155	C₁₃×C₂²⋊C₄	—	2	8	no	—
156	C₁₃×C₂²⋊C₄	—	2	8	no	—
157	C₁₃×C₂²⋊C₄	—	2	8	no	—
158	C₁₃×C₂²⋊C₄	—	2	8	no	—
159	C₄²×C₁₃	—	2	8	no	—
160	C₄²×C₁₃	—	2	8	no	—
161	C₄²×C₁₃	C₂×D₄	1	4	yes	—
162	C₄²×C₁₃	C₂×D₄	1	2	yes	—
163	C₄²×C₁₃	C₂⁴	1	2	yes	—
164	C₄²×C₁₃	C₂⁴	1	4	yes	—
165	C₂×#556	C₂×C₁₃	1	2	yes	complemented
166	#3402	C₂×C₁₃	1	16	yes	direct product factor
167	C₂×#497	C₂×C₁₃	1	2	yes	complemented
168	C₂×#495	C₂×C₁₃	1	1	yes	characteristic
169	C₂×#464	C₂×C₁₃	1	2	yes	complemented
170	C₂×#462	C₂×C₁₃	1	2	yes	complemented
171	C₂×#463	C₂×C₁₃	1	2	yes	—
172	C₂×#446	C₂×C₁₃	1	1	yes	characteristic, complemented
173	C₂×#440	C₂×C₁₃	1	2	yes	complemented
174	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂³×C₁₃	—	2	4	no	—
176	C₂³×C₁₃	—	4	4	no	—
177	C₂³×C₁₃	—	4	4	no	—
178	C₂³×C₁₃	—	4	4	no	—
179	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₃	—	2	4	no	—
181	Q₈×C₁₃	—	2	4	no	—
182	Q₈×C₁₃	—	2	4	no	—
183	Q₈×C₁₃	—	2	4	no	—
184	Q₈×C₁₃	—	4	4	no	—
185	Q₈×C₁₃	—	4	4	no	—
186	Q₈×C₁₃	—	4	4	no	—
187	D₄×C₁₃	—	2	4	no	—
188	D₄×C₁₃	—	2	4	no	—
189	D₄×C₁₃	—	4	4	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	4	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	4	no	—
197	C₂×C₄×C₁₃	—	4	16	no	—
198	C₂×C₄×C₁₃	—	4	4	no	—
199	C₂×C₄×C₁₃	—	4	4	no	—
200	C₂×C₄×C₁₃	—	4	4	no	—
201	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
203	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
205	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
207	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
208	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
209	C₈×C₁₃	—	2	2	no	—
210	C₈×C₁₃	—	2	4	no	—
211	C₈×C₁₃	C₂×#41	1	4	yes	—
212	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
213	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
214	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
215	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
216	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
217	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
218	#556	—	2	8	no	—
219	#556	C₂²×C₁₃	1	16	yes	complemented
220	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
221	C₂×#126	—	2	2	no	—
222	C₂×#126	—	2	2	no	—
223	C₂×#124	C₂²×C₁₃	1	2	yes	—
224	C₂×#124	C₂²×C₁₃	1	2	yes	—
225	C₂×C₂²⋊Q₈	—	2	2	no	—
226	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
227	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
228	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
230	C₂×#117	—	2	2	no	—
231	#497	C₂²×C₁₃	1	16	yes	complemented
232	#495	C₂²×C₁₃	1	8	yes	—
233	#464	C₂²×C₁₃	1	16	yes	complemented
234	#463	C₂²×C₁₃	1	16	yes	—
235	#462	C₂²×C₁₃	1	16	yes	complemented
236	#446	C₂²×C₁₃	1	8	yes	complemented
237	#440	C₂²×C₁₃	1	16	yes	complemented
238	C₄×Q₁₆	C₂²×C₁₃	1	8	yes	complemented
239	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
241	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
242	C₂×#103	C₂²×C₁₃	1	2	yes	—
243	C₂×#103	C₂²×C₁₃	1	2	yes	—
244	C₂×#102	C₂²×C₁₃	1	2	yes	—
245	C₂×#97	C₂²×C₁₃	1	2	yes	—
246	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×C₁₃	—	4	4	no	—
248	C₂²×C₁₃	—	4	4	no	—
249	C₂²×C₁₃	—	4	4	no	—
250	C₂²×C₁₃	—	8	8	no	—
251	C₂²×C₁₃	#550	1	2	yes	—
252	C₂²×C₁₃	#575	1	2	yes	—
253	C₂²×C₁₃	#578	1	2	yes	—
254	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
255	C₄×C₁₃	—	2	4	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	2	2	no	—
258	C₄×C₁₃	—	2	4	no	—
259	C₄×C₁₃	—	4	4	no	—
260	C₄×C₁₃	—	4	4	no	—
261	C₄×C₁₃	—	4	4	no	—
262	C₄×C₁₃	#550	1	2	yes	—
263	C₄×C₁₃	C₂²×#41	1	1	yes	characteristic
264	C₄×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
265	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
266	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
267	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
268	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
269	C₂³×C₄	—	2	2	no	—
270	C₂×Q₁₆	—	2	4	no	—
271	C₂×Q₁₆	—	4	2	no	—
272	C₂×Q₁₆	—	4	4	no	—
273	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
274	C₂×Q₁₆	C₂³×C₁₃	1	4	yes	—
275	C₂×Q₁₆	C₂³×C₁₃	1	8	yes	—
276	C₂×SD₁₆	—	2	8	no	—
277	C₂×SD₁₆	—	4	4	no	—
278	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
279	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
280	C₂×D₈	—	4	2	no	—
281	C₂×D₈	C₂³×C₁₃	1	4	yes	—
282	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
284	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
285	C₄⋊Q₈	—	2	4	no	—
286	C₄⋊Q₈	C₂³×C₁₃	1	8	yes	—
287	#126	—	2	16	no	—
288	#126	—	2	16	no	—
289	#124	—	2	4	no	—
290	#124	—	2	4	no	—
291	#124	C₂³×C₁₃	1	8	yes	—
292	#124	C₂³×C₁₃	1	8	yes	—
293	C₂²⋊Q₈	—	2	16	no	—
294	C₄×Q₈	—	2	4	no	—
295	C₄×Q₈	—	2	4	no	—
296	C₄×Q₈	D₄×C₁₃	1	4	yes	—
297	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
298	C₄×Q₈	C₂³×C₁₃	1	8	yes	—
299	C₄×Q₈	C₂³×C₁₃	1	4	yes	—
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	C₂³×C₁₃	1	8	yes	—
302	#117	—	2	16	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
308	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
318	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
319	#107	C₂³×C₁₃	1	4	yes	—
320	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
321	C₄⋊C₈	C₂³×C₁₃	1	4	yes	—
322	#103	C₂³×C₁₃	1	8	yes	—
323	#103	C₂³×C₁₃	1	8	yes	—
324	#102	C₂³×C₁₃	1	8	yes	—
325	#97	C₂³×C₁₃	1	8	yes	—
326	C₄×C₈	C₂³×C₁₃	1	4	yes	—
327	C₂×C₁₃	—	8	4	no	—
328	C₂×C₁₃	#3402	1	4	yes	direct product factor
329	C₂×C₁₃	C₂×#550	1	1	yes	characteristic
330	C₂×C₁₃	C₂×#575	1	1	yes	characteristic
331	C₂×C₁₃	C₂×#578	1	1	yes	characteristic
332	C₂⁴	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	4	2	no	—
340	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
341	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
342	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	8	no	—
351	C₂²×C₄	—	4	8	no	—
352	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
357	Q₁₆	—	2	8	no	—
358	Q₁₆	—	4	4	no	—
359	Q₁₆	—	4	8	no	—
360	SD₁₆	—	2	16	no	—
361	SD₁₆	—	4	8	no	—
362	D₈	—	4	4	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	4	no	—
365	C₂×C₈	C₁₃×#41	1	4	yes	—
366	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
367	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
368	C₂×C₈	C₂⁴×C₁₃	1	2	yes	—
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	8	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	C₂×D₄×C₁₃	1	8	yes	—
375	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
376	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
377	C₂²⋊C₄	—	2	8	no	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₄²	—	2	8	no	—
383	C₄²	—	2	8	no	—
384	C₄²	C₂×D₄×C₁₃	1	4	yes	—
385	C₄²	C₂×D₄×C₁₃	1	2	yes	—
386	C₄²	C₂⁴×C₁₃	1	2	yes	—
387	C₄²	C₂⁴×C₁₃	1	4	yes	—
388	C₁₃	C₂×#3402	1	1	yes	characteristic, direct product factor, Sylow
389	C₂³	—	2	4	no	—
390	C₂³	—	4	4	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	4	no	—
393	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
394	Q₈	—	2	4	no	—
395	Q₈	—	2	4	no	—
396	Q₈	—	2	4	no	—
397	Q₈	—	2	4	no	—
398	Q₈	—	4	4	no	—
399	Q₈	—	4	4	no	—
400	Q₈	—	4	4	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	4	no	—
403	D₄	—	4	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	4	16	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
416	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
417	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
419	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
421	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
422	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	2	4	no	—
425	C₈	C₂×C₁₃×#41	1	4	yes	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	8	8	no	—
430	C₂²	C₁₃×#550	1	2	yes	—
431	C₂²	C₁₃×#575	1	2	yes	—
432	C₂²	C₁₃×#578	1	2	yes	—
433	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	4	no	—
438	C₄	—	4	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	4	no	—
441	C₄	C₁₃×#550	1	2	yes	—
442	C₄	C₂²×C₁₃×#41	1	1	yes	characteristic
443	C₄	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
444	C₂	—	8	4	no	—
445	C₂	C₁₃×#3402	1	4	yes	direct product factor
446	C₂	C₂×C₁₃×#550	1	1	yes	characteristic
447	C₂	C₂×C₁₃×#575	1	1	yes	characteristic
448	C₂	C₂×C₁₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₁₃×#556	C₂	semidirect
2. C₁₃×#3402	C₂	direct (N × H)
3. C₂×C₁₃×#497	C₂	semidirect
5. C₂×C₁₃×#464	C₂	semidirect
6. C₂×C₁₃×#462	C₂	semidirect
8. C₂×C₁₃×#446	C₂	semidirect
9. C₂×C₁₃×#440	C₂	semidirect
10. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
18. C₁₃×#556	C₂²	semidirect
30. C₁₃×#497	C₂²	semidirect
32. C₁₃×#464	C₂²	semidirect
34. C₁₃×#462	C₂²	semidirect
35. C₁₃×#446	C₂²	semidirect
36. C₁₃×#440	C₂²	semidirect
37. C₄×C₁₃×Q₁₆	C₂²	semidirect
108. C₂×#3402	C₁₃	direct (N × H)
165. C₂×#556	C₂×C₁₃	semidirect
166. #3402	C₂×C₁₃	direct (N × H)
167. C₂×#497	C₂×C₁₃	semidirect
169. C₂×#464	C₂×C₁₃	semidirect
170. C₂×#462	C₂×C₁₃	semidirect
172. C₂×#446	C₂×C₁₃	semidirect
173. C₂×#440	C₂×C₁₃	semidirect
174. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
219. #556	C₂²×C₁₃	semidirect
231. #497	C₂²×C₁₃	semidirect
233. #464	C₂²×C₁₃	semidirect
235. #462	C₂²×C₁₃	semidirect
236. #446	C₂²×C₁₃	semidirect
237. #440	C₂²×C₁₃	semidirect
238. C₄×Q₁₆	C₂²×C₁₃	semidirect
328. C₂×C₁₃	#3402	direct (N × H)
388. C₁₃	C₂×#3402	direct (N × H)
445. C₂	C₁₃×#3402	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#556	2
C₁₃×#3402	2
C₂×C₁₃×#497	2
C₂×C₁₃×#495	2
C₂×C₁₃×#464	2
C₂×C₁₃×#462	2
C₂×C₁₃×#463	2
C₂×C₁₃×#446	2
C₂×C₁₃×#440	2
C₂×C₄×C₁₃×Q₁₆	2
C₂×#3402	13

Subgroups — C2×C13×#3402 #15747738

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#3402 #15747738